# Metabolic perturbation studies using a Nash Equilibrium model of liver machine perfusion: modeling oxidative stress and effect of glutathione supplementation

## TL;DR

This paper uses a mathematical model to study liver preservation during machine perfusion and finds that glutathione and temperature control can reduce oxidative stress.

## Contribution

A novel Nash Equilibrium and Monte Carlo optimization model is developed to determine optimal liver preservation strategies and glutathione requirements.

## Key findings

- Minimum glutathione requirements increase with higher hydrogen peroxide concentrations.
- High hydrogen peroxide levels cause cytochrome C dysfunction, reducing ATP synthesis and energy charge in liver cells.
- Optimal gradual warming temperature policies can minimize oxidative stress during liver perfusion.

## Abstract

The current clinical standard of Static Cold Storage (SCS) which involves preservation on ice (about +4°C) in a hypoxic state limits storage to a few hours for metabolically active tissues such as the liver and the heart. This period of hypoxia during can generate superoxide and other free radicals from purine metabolism, a well-established component of ischemia/reperfusion injury (IRI). Machine perfusion is at the cutting edge of organ preservation, which provides a functional, oxygenated preservation modality that can avoid/attenuate IRI. In clinical application, perfusion usually follows a period of SCS. This presentation of oxygen following hypoxia can lead to superoxide and hydrogen peroxide generation, but machine perfusion also allows manipulation of the temperature profiles and supply of antioxidant treatments, which could be used to minimize such issues. However, metabolomic data is difficult to gather, and there are currently no mathematical models present to allow rational design of experiments or guide clinical practice. In this article, the effects of a gradual warming temperature policy and glutathione supplementation to minimize oxidative stress are studied. An optimal gradual warming temperature policy for mid-thermic machine perfusion of a liver metabolic model is determined using a combination of Nash Equilibrium and Monte Carlo optimization. Using this optimal gradual warming temperature policy, minimum GSH requirements to maintain hydrogen peroxide concentrations in the normal region are calculated using a different Monte Carlo optimization methodology. In addition, the dynamic behavior of key metabolites and cofactors are determined. Results show that the minimum GSH requirement increases and that the ratio of GSH/GSSG decreases with increasing hydrogen peroxide concentration. In addition, at high concentrations of hydrogen peroxide it is shown that cytochrome C undergoes dysfunction leading to a decrease in useful oxygen consumption and ATP synthesis from the electron transport chain and an overall reduction in the energy charge for the liver cells.